A vehicle is well-known that provides engine stop control of stopping an engine in operation when an automatic stop request is made in a state in which no engine power is required such as when the engine simply idles while the vehicle is stopped or when a hybrid vehicle is switched from engine running to motor running, for example. This corresponds to a vehicle described in Patent Document 1, for example. Patent Document 1 proposes that while an engine is in transition to a rotation stop state in association with provision of the engine stop control, if a restart request is made such as turning-on of an accelerator and turning-off of a brake, a restart control is initiated to restart the stopping engine even before the engine completely stops rotating.